The winger was forced off just eight minutes into the La Liga side's Champions League win over Schalke 04 at the Bernabeu.
In his post-match press conference, manager Carlo Ancelotti said: "We will lose a very important player who has played well this season but this is football.
"The dressing room is affected by his injury. We feel very sad. This happens in football, but we have to stay positive."
The 21-year-old's agent confirmed shortly after the match that an MRI scan revealed that Jese has a complete tear in his right knee, and will face a six- to eight-month recovery period.
It is expected that Jese will undergo surgery later this week.